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Fun teaching resources & tips to help you teach math with confidence

Math Strategies: Problem Solving by Drawing a Picture

I am a very visual learner . Whenever I am facing a word problem of any kind, my initial reaction is to draw a picture. Even if it is a fairly simple problem and I think I already know how to solve it (or even already know the answer), I will almost always still draw a picture . but even if you don’t think of yourself as a “visual learner,” drawing pictures (or other visuals) is still one of the most powerful strategies. Brain research shows that when solving math problems, the ‘visual’ parts of our brain light up, even when we don’t draw a picture! So rest assured, problem solving by drawing a picture is helpful for any student!

–>Pssst! Do your kids need help making sense of and solving word problems? You might like this set of editable word problem solving templates ! Use these with any grade level, for any type of word problem :

Solve Math Problems by Drawing a Picture: 

Maybe I’m drawn to this strategy because I’m such a great artist…no, that’s definitely not it! I believe it is because seeing a visual representation of the problem can put things in perspective, help organize the information, and enable students to make connections that may not have been otherwise seen.

Because of the impact of visuals on our brain and our learning, this is an important and helpful problem solving strategy . Especially if you are stuck and don’t know where to go or what to do. Then you have nothing to lose, right?

When I was teaching high school, I would often encourage students to draw a picture when working on distance/rate/time problems .

It is very easy to get bogged down in all the details and numbers, especially if the problem includes unnecessary information (details that you don’t really need to know in order to solve it). Wading through everything you’re given and making sense of what’s important can be easier when you draw a picture!

It’s also incredibly important to draw a picture when working on geometry tasks, such as   Pythagorean theorem problems or similar triangles and indirect measurement . Even if you know how to solve it without a picture, you will greatly increase you chances of a careless mistake if you don’t take the extra five seconds to draw a picture.

One important thing to remember, however, is that the picture does not need to be pretty . In fact, in some cases it may not even be a picture, just a visual representation of the information.

And that’s ok! The point is to help you solve the math problem , not to win an art award. ( Thank goodness, because seriously, I’m no artist! ).

If you would like to discuss this strategy with your students and help encourage them to use it when appropriate, I’ve created a short set of problems to do just that!

These word problems could be used with grades 2-4 and include a page that specifically states, “Draw a picture…” and then another page of problems were it would be useful to draw a picture, but it is not explicitly stated.

The goal is to get students used to organizing the information in a meaningful way to help them better think about and/or solve the problem.

{Click HERE to go to my shop and download the Problem Solving by Drawing a Picture Practice Problems !}

What do you think? Do you use this problem solving strategy or encourage your students to try it? Do you think it’s helpful?

Here are the other articles in this series on problem solving: 

• Problem Solve using Guess and Check
• Problem Solve by Finding a Pattern
• Problem Solve by Making a List
• Problem Solve by Solving an Easier Problem
• Problem Solve by Working Backwards

Thanks so much for your Math freebie. Drawing pictures is a great way to access student understanding. Arlene LMN Tree

Thanks Arlene! Yes, I agree! Students have to show what they know to be able to draw an appropriate picture and solve. Thanks for stopping by! 🙂

• Pingback: Problem Solving Strategy: Draw a Picture - Teach Junkie
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Teaching Math Word Problems with Pictures

Help your students visualize their answers.

If you google word problem jokes, this one will pop up a lot:

“If you have 4 pencils and I have 7 apples, how many pancakes will fit on the roof?

Purple, because aliens don’t wear hats.”

It’s hilarious because it’s true! Many of our students see nonsense in word problems. They not only have to figure out what the word problem is asking them to do, but then they have to actually solve it. It’s a process. However, if we want them to internalize the concept, not just the numbers, pictures can help! Visuals can help students comprehend meaning when the words aren’t making sense to them. Don’t underestimate the power of teaching word problems with pictures. Here are a few easy ways to incorporate visuals into everyday math:

The power of “acting it out”

Before you go from manipulatives to drawing, try having students act out problems. If the problems involve eating, bring in food and have a student actually act like they are in the story problem. If the problem involves a specific number of boys and girls, have that many students get up and show the class what is going on in the problem. Taking this step will help students visualize the problem and think about the actions rather than just guessing if they should add, subtract, multiply, or divide.

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Getting ready to draw

When you’re ready to start solving word problems with pictures, follow Jan Rowe’s steps :

• Read the entire problem: Get all the facts and underline keywords.
• Answer the question: What am I looking for?
• Draw a picture or diagram: Visualize as a real-world situation.
• Solve the problem: Set up the equation and solve.
• Check your solution: Is this answer reasonable?

Drawing as a step of the process

Visual representations are a good starting point for word problems because it is an intermediate step between language-as-text and the symbolic language of math . Drawing lowers the affective filter because it can be less stressful. We aren’t stepping straight into that equation; we are just drawing to figure out what the question is actually asking us. Remind students that we are not in art class. It is perfectly OK for your math pictures to be just scribbles as long as you know what they represent. Another great perk of the “Draw a Picture” strategy is that you, as a teacher, can really step inside the student’s brain to see how their mathematical brain works. Encourage labeling so that you can catch misconceptions right away. These drawings can lead to great math talk conversations, which build that academic language that we all want to hear.

Jayden had two boxes of books with twelve books in each box. He gave four books to his sister. How many books did Jayden keep for himself?

Draw a picture:

Try photography instead of drawing

Story problems are grounded in reading. Photograph Math is an activity that can help visual learners grasp the math skill first, then add in the language. All you’ll need is a camera (or phone) to take pictures. Here’s how it works:

• Students brainstorm the ways in which, and the places where, they use math.
• They stage a photograph representing one of these ideas.
• Students write their own real-life word problems to go with their posed photograph(s).
• Students take a photograph of the menu inside the cafeteria. They write problems that help them figure out how much money they need to get specific lunches, snacks, or drinks. Extension: Think about how much you would need to get a snack every day, for a week, etc.
• Someone might take a photo of a number on a library book. Then try to figure out what value that number would have based on the number of digits and round the number to the nearest whole, tenths, or hundredth.
• Students take a photo of your stash of whiteboards markers. They could write problems about the amount of each color you have. They may choose to think about what happens if another teacher borrows a certain number of markers, etc.

Photograph math can help students to start thinking like a mathematician in all aspects of life. If students begin to see the math around them, then they can truly begin to comprehend the story problems that we present to them in class.

Read a math picture book

Remember when I said story problems are grounded in reading? Why not use actual stories? Children’s picture books can provide a rich context from which to begin mathematical investigations . As students see math concepts play out in stories and illustrations, they are engaged and better able to construct meaning. Seeing the problem-solving process in action through a book can serve as a model for students when they go off on their own to solve problems. Here is a list of 16 picture books about math .

Assign math as picture prompts

Consider starting each week with a relevant picture prompt. Sometimes, the picture is of a mathematical error we came across in real life. The challenge to students is to figure out the mistake. Other times, we simply provide an image and challenge students to come up with a story problem to accompany it. Giving students ownership of these problems can strengthen and extend their comprehension of story problems.

• Put up a sign of a price mistake in a store. Then write on the board: “Ms. Caudill saw this sign at Walmart this weekend and laughed. Why? How might you fix it?”
• Show students the following prompt: Write a story problem using the photo and the following word bank: apples, tomatoes, sweet potatoes, pound, gallon, farmer’s market.

The truth is, story problems are challenging for all students. We have to find ways to make the story problems relative to students’ lives if we want them to succeed.

How do you teach word problems with pictures? Share in the comments below.

Want even more strategies for teaching word problems check out 14 effective ways to help your students conquer math word problems ., want more articles like this make sure to sign up for my weekly newsletter for third grade teachers .

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35 Effective Problem-Solving Products With Gasp-Worthy Review Photos

These things work and have photographic evidence to prove it.

BuzzFeed Staff

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Juno & Co.  is a small business specializing in personal care and skincare products. 

Promising review: "I LOVE THIS PRODUCT!!!! I found it on TikTok, and OMG!! It works so well. I don't have to sit there and rub the crap out of my eyelashes to get the waterproof mascara off. I will admit it doesn't take 100% of the makeup off, but about 95% of my makeup comes off. It is not water-resistant, as emulsifying it with water helps take the makeup off. I have not found a better makeup remover, and yes, that includes Micellar Water (which also works well but leaves my skin feeling oily).  With this cleansing balm, my face feels hydrated and smooth. LOVE LOVE LOVE IT!!!!!!!! 1000/10 would recommend!!!" — Deetje Frederick

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The cleanser is nonabrasive, bleach-free, and effective on stainless steel, porcelain, ceramic, copper alloys, fiberglass, Corian, brass, bronze, chrome, and aluminum surfaces. Simply wet the surface to be cleaned, sprinkle a small amount of cleanser on the surface, and gently rub it with a wet cloth or sponge. Rinse thoroughly within one minute of application and wipe it dry.

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10. A Clorox toilet scrubbing wand (the magic kind, maybe?) that'll turn your yuckiest toilet into something usable again. The disposable pads come pre-soaked in cleaning solution to make things easier.

This wizardly kit comes with one wand, a caddy, and six disposable scrubber refills.

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11. A Shark Tank -approved tattoo aftercare salve  you should really consider if you want to protect your new investment. It's designed with just seven vegan ingredients to soothe, protect, and enhance your ink, no matter how long you've been working on completing that sleeve. 

Mad Rabbit is a small biz found by college friends Oliver Zak and Selom Agbitor after seeing a gap in the market for all-natural products to heal, protect and enhance tattoos. They pitched their tattoo salve in season 12 of Shark Tank.

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12. A set of drill brushes so effective, you'll be shocked how clean your home used to be. Why spend the energy scrubbing when pressing a drill button will do the trick? It's so important to delegate.

The set comes with a 2-inch flat brush, a 4-inch flat brush, and a round brush. The drill isn't included, but you can grab a basic Black and Decker one ( $27.83 on Amazon) that'll do the trick.

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Get it from Amazon for $14.95 (available in six colors and stiffness levels).

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Get it from Amazon for $23.42 (available in six packs).

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Make sure you read all the directions before using it so you don't accidentally give yourself a hickey. I've used this, and it really works!

Promising review : "I am a magnet for bites of all kinds and carry topical and medicines with me at all times — so I figured this would be a good product to see if it really works. I woke up with a bug bite on my arm, so I used this little tool (three times per the instructions) —  immediately after using it, it stopped itching! And less than 24 hours later, the bump/bite gone! There is a very faint red mark from using the thing, but a small price to pay IMO. Bottom line: it’s awesome. I’m carrying it with me everywhere!" — Rebecca

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Just fill your dirty mug with water, add a tablet, let fizz for half an hour, and then rinse!

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Check out our closer look at these Bottle Bright tablets for more incredible before and afters.

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Don't use these medicated pads on irritated, red, or infected skin. And only use these for warts — no ingrown hairs, genital warts, or moles.

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Promising review: "This is a wonderful product. I have an older dog who can't always wait until I get home from work, so accidents occasionally happen. I have a Hoover Rug Scrubber , and this product is very easy to use with my machine. Carpet Miracle works amazingly well on stains and odors, even those that have set for a while. I did the carpet in the 'room of shame' twice just to be sure, although for normal soil and odors, once should be more than enough. It leaves behind a wonderful clean, fresh scent, and the carpet feels and looks wonderful. I plan on continuing to use this product to keep my carpets clean and my home smelling fresh." — Vicky Faurot

Get it from Amazon for $19.97 .

20. A bottle of sulfate-free biotin shampoo  that thousands of reviewers have said helped volumize their hair. The biotin can help fill out thinning hair and the nourishing ingredients like rosemary oil, zinc, and coconut oil can help moisturize. 

Read more about how biotin shampoo could help with the fullness of hair at Cleveland Clinic .

Maple Holistics is a small business that specializes in beauty products with all-natural ingredients. Check out a TikTok of the biotin shampoo in action. 

Promising review: "I love this shampoo! I had gastric sleeve surgery, and my hair was very, very thin. I started taking biotin and switched to biotin shampoo, as recommended by my doctor. It doesn’t make your hair grow by washing it, but it makes your hair and roots stronger. And it worked. After using the whole bottle, my hair was stronger. I had a lot of new growth that was sticking around (the previous new growth fell out early on), and my hair was getting thicker. Eight months later, my hair is back to normal. It's longer and thicker than ever."  — Diane J. Huff

Get it from Amazon for $12.95  (available in three scents).

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The pen is filled with a cleaning and polishing solution to remove clouding dirt and oil, leaving gems shiny. Just twist the bottom of the pen to dispense the fluid and brush on.

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Prime members: You can  try before you buy !

Reviewers swear these don't even have a break-in period , making them a great pick for that last-minute outdoorsy trip where hiking and rough terrain are on the docket. Note that  it's recommended to go up a half size in these boots to accommodate thicker hiking socks. 

Promising review : "There’s a reason that these hiking boots are the #1 best hiking boots on Amazon. I am amazed that they are so comfortable. This is day four that I’ve worn them, and my feet feel fantastic! I hiked four miles on the second day, and my feet were not tired, achy, or sore. I have been hiking for 30 years and have had numerous boots, but not a single pair has been this comfortable.  The price is so worth it for what you get." — Granny B

Get them from Amazon for  $49+  (available in sizes 5–12, including wide sizes, and 16 colors). You can find a similar men's version  here .

24. A set of OXO's amazing pop containers so you can keep your dry food and ingredients fresh and pest-free longer. They'll also make your pantry look a lot less chaotic.

These sleek-looking containers keep food fresh and presentable, so you don't have to get a lecture when your mom visits and peeks into your cabinets. They come in a variety of shapes and sizes to accommodate your various needs. So far, I've used them for sugar, flour, cornmeal, Wheat Thins, spaghetti, pretzels, and almonds. Each container has a big button on top that you can press to open or seal the jar. It's so satisfying to pop these things open that I can't imagine using a different container system ever again.

Get them from Amazon: the five-piece set for $49.95 and the 10-piece for $112.95 .

25. A leather cleaner to bring your furniture, car seats, bags, shoes, and more back to usable condition. The solution conditions, cleans, and restores — so maybe you don't need to buy a new couch after all.

Promising review: "I've used this on all of my favorite shoes and boots. Then I used it on my purse. It's enjoyable seeing how much improvement you can see on beat-up leather. The scent is what sold me on this product. I loved that it was an almond scent. But the results are so much better. It took about two minutes to clean them up. Highly recommended. Also, their customer service is top-notch." — RileyD

Get it from Amazon for $34.15 .

26. A tote organizer that has two vital functions: 1. brings order to your chaotic bag that weirdly has no pockets, and 2. lets you transport all your stuff with one fluid motion. It adds a whopping 13 pockets and a detachable middle pouch for valuables.

Measure your bag to make sure it's a good fit!

Promising review: "This thing is great! I have a large bag I use as a carry-on when I fly by plane. Unfortunately, it has very few pockets and is just like a bottomless pit. This fit in perfectly. I was able to organize all my items quite well. They were easy to retrieve in flight and in the airport. I didn't use the zipper compartment at all but put that piece in to use it as a divider. It is well-made and sturdy. Be sure to measure your inner bag space first!" — Susan

Get it from Amazon for $19.88+ (available in five sizes and 13 colors).

27. A  shoe stretch spray  if you have a pair of gorgeous loafers or boots you love but never wear...because of the agonizing pain that comes with it. This spray will gradually stretch them out without staining or fading and is likely more effective than the freezer trick. 

BuzzFeed Shopping editor  Amanda Davis  swears by this spray. Check out her Foot Matters Shoe Stretch spray review  for more details! BTW, Foot Matters is a small business that specializes in shoe-stretching products.  

Promising reviews: "My sandals were awfully tight on the top of my feet. I tried everything before finally finding this spray. Nothing helped; there was no relief. Then I tried this spray, and it moved heaven and earth, and now my sandals are perfect! " — Swissharpist

"I injured my foot a few months back, and most of my shoes don't fit. I've tried stretchers, hair dryer, wearing multiple socks — everything. I bought this stuff, and within a half hour, my problems were solved . Try this method first." — Susan Olson

Get it from Amazon for $9.99 . 

28. A privacy window film that's easy to install and fills your home with lots of rainbows when the sun hits it just right. Now you can sing "somewheeeere over the rainbow" as you step over your dog.

Read more about this beloved rainbow window film .

Promising review: "I initially purchased this window film to use to brighten up my classroom. That film has lasted over two years! I enjoyed it so much that I bought another roll to use in my home. I would recommend using a spray bottle and a credit card-like object for application. Go slowly, one area at a time, to minimize bubbles as much as possible. My classroom ones have quite a few bubbles (user error), but that has not caused them to fall off, which has been very nice." — Kris H.

Get it from Amazon for $13.98+ (available in nine sizes).

29. A foaming lavender bath with pure epsom salt to soothe the body and create the most sudsy bath experience ever.

While you're in that extra deep bath, you might as well go all out and add some bubbles.

Promising review: "I love this stuff soooo much. I have had some rash issues on my fingers ever since I got a full-body rash from Downy Unstopables and had to take prednisone to get rid of it. Ever since I started regularly soaking in the tub with this, I have had hardly any flare-ups. Something about the ingredients in this particular combination makes my skin sing. Plus, it smells amazing and provides top-notch bubbles. Worth every penny. "— Sarah

Get it from Amazon for $6.69 .

30. A c ruelty-free Essence Lash Princess lengthening mascara that's lightweight, won't transfer, doesn't smudge, and lasts all day — oh, and makes your eyelashes look like tall, beautiful skyscrapers.

Promising review: "Love this mascara! I’ve used the 'best of the best' designer, super hyped, ultra-popular mascara available, and NOTHING compares to this stuff ! I don’t even bother using a lash curler anymore! I buy two at a time so I always have a spare (yes, it’s that good!!). I highly recommend this particular mascara... it goes on effortlessly, it lasts pretty much all day, and the price — I feel like I’m almost stealing it! I’d give it 10 stars if I could!!! " — chulaboola

Get it from Amazon for $4.99 .

31. A container of oatmeal paw butter to soothe and relieve your dog's cracked, dry paws. Its eco-friendly formula is pH-balanced so it's safe for cats, even if licked or swallowed. *seriously considers licking it myself to see if it really tastes like oatmeal*

Promising review:  "My dog's paws are extra soft, bringing back memories of when he was a puppy. My dog did not lick it, but I’m sure some dogs will. I recommend putting it on at night, so the oils do not get on your floors. In the morning, it is dry, and you we love to touch your dog's paws." — Joshua Torres

Get it from Amazon for $7.59+  (available in two sizes and scents).

32. A robot vacuum happy to do all the hard work for you. Just turn it on and watch someone else vacuum for a change. This device earned over 9,000 5-star reviews by being affordable, powerful, and able to reach tight corners.

This device is quiet, self-recharging, uses an infared-sensor to expertly maneuver around obstacles. And it comes with a 12-month warranty in case anything happens.

Promising review: "After running Eufy for nearly two months now, I can confidently say I absolutely LOVE it! It is amazing on my hardwood floors. It picks up sooo much fine dust brought in by my two German shepherds! They shed year-round! And it’s super effective with pet hair! Wow! I use Eufy once a day for a little more than hour, emptying and cleaning the brushes out about three to four times during use. It seriously has been life-changing, keeping my floors cleaner than sweeping! Great purchase and I would highly recommend!!" — Jacqueline M

Get it from Amazon for $249.99+  (available in three versions).

33. A box of Color Catcher sheets to prevent the dreaded "all my clothes are now pink from this one stray red sock" debacle. These handy sheets are designed to grab any dye that leaks or bleeds so you can keep enjoying your white tees.

Promising review: "These Color Catcher sheets really protect colors from bleeding. It makes all clothes/laundry brighter and looking like new — not that old washed color after just one wash without these sheets. I give this product 5+ stars. Highly recommend. A few pennies spent additionally on your laundry makes one look like wearing new clothes all the time." — Nikita

Get 72 sheets from Amazon for $10.95 .

34. A hairbrush cleaning tool  perfectly designed to remove hair, debris, fuzz, fur, dandruff — I could go on. OK, you see how this thing is very needed, right? 

The pointed end of the tool is ideal for picking out tangles, the stiff bristles work great at removing dust and dirt, and the bristles at the bottom end of the tool can give your hairbrush a deep clean.

Promising review: "When I bought this, I was really skeptical. I am grossed out by my hairbrush and clean it all the time. I've soaked it in vinegar and tea tree oil, used a toothbrush, scrubbed it with shampoo, picked it clean by hand — everything you can think of. Still, it's so hard to get the little lint that forms at the base of the brush — they don't dissolve off, and you have to pick them off the bristles one by one because a toothbrush won't even break them up. This thing works amazingly. I don't know why, it just does — the particular texture of the bristles on this really grabs everything. It scraped the little lint rings right off, and now my brush is cleaner, 10 times as fast." — HeartsofHavoc

Get it from Amazon for $11.95 .

35. A  multi-purpose cleaning paste to help you get your oven into tip-top shape in no time at all. It's made in small batches with natural ingredients, so it's safe for your family, pets, and home. Use it on your oven, stovetop, bathroom tiles — or even your produce and hands. 

BuzzFeed Shopping editor  Danielle Healy swears by this cleaning paste: "I recently moved into a new apartment, so lately I've been cleaning A LOT. Shortly after moving in, my partner and I went to store something on the top of the kitchen cabinets, only to find them caked in a thick layer of grime. 🤢 After going at it with regular multipurpose cleaner (with little success), we broke out the scour paste as a last-ditch effort, and OH BOY did this miracle product deliver (pics above). If it can handle that grossness, it's going to have no problem with day-to-day messes like soap scum and burnt-on food. Plus, it smells delightful and comes in minimal, low-waste packaging!"

Promising review : "Buyer beware: don’t buy just one!! Learn from my mistake, and buy at least two jars because this stuff is INCREDIBLE. I used it on my textured shower floor. It was EASIER to clean and required less scrubbing than any other product I’ve used , including CLR. If you have black matte bathroom fixtures, this is the stuff you need. My shower and sink drains look brand new. My other favorite part about this scour paste is the fact that I don’t need to use any paper towels. Just a wet rag to wipe it all down at the end. I will be buying more jars for myself and to give to my friends because this stuff is absolutely amazing. You won’t regret it!" — littleashleyshortcak

Get it from Humble Suds on Etsy for $15.95+ (available in two sizes/packaging materials). 

Reviews have been edited for length and/or clarity.

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